Stats 4#

STAT 1430 Recitation 4 Correlation and Regression Part 1: Correlation 1. Write down a data set that contains 5ive (x, y) points whose correlation is EXACTLY NEGATIVE ONE (-1). Hint: A scatterplot might help. Properties of correlation. See your lecture notes. Looking at the formula on the formula sheet for r may help, but also consider the statistical reasons for your answers, not solely math. 2. Correlation has . a) The same units as the data b) No units 3. When 5inding the correlation between two quantitative variables, you will get the same answer if you switch X and Y. Explain brie5ly. (See lecture notes) Yes you will get the same answer regardless of axis labels. The commutative property ensures that mixing up the axis won’t effect the outcome ( 5 times 9 and 9 time 5 or both 45 regardless) 4. Scatterplots examine relationships between what type(s) of variables? a) Categorical b) Quantitative c) Both categorical and quantitative variables 5. Correlation is affected by outliers. Explain why, brie5ly. Yes, the correlation is affected by the outliers since the formula revolves around means and standard deviations which are heavily inOluenced by outliers and skewness 6. Correlation is a measure of the strength and direction of what type of relationship between two quantitative variables? _______Linear_______________________ 7. Correlation of a sample (r) will always be a number between -1 and 1 Bob wants to use house size to predict house price in Columbus. He starts out by making a scatterplot of data from 100 homes randomly selected from the current Columbus market. In this case: 8. On Bob’s scatterplot, which variable makes the most sense to appear on the X axis? Data Point X value Y value 1 5 9 2 6 8 3 7 7 4 8 6 5 9 5 1

STAT 1430 Recitation 4 Correlation and Regression House size would be best Oit for the x - axis The following scatter plot shows the relationship between vocabulary size and age. The variables vocabulary size and age have a correlation of 0.96. Answer the following questions based on the known facts. 9. True/false: Having a correlation of positive 0.96, means that there is a 96% chance that a subject at age 4 will have a vocabulary size of 1500 words. a) True b) False 10. True/false: The correlation of positive 0.96, means that 96% of the subjects observed had a vocabulary size that was greater than their age. a) True b) False NOTE: Correlation does NOT ALWAYS imply Causation, which says that a correlation between two variables does not always mean that a change in one variable causes a change in the other (there could be other reasons the data has a good correlation). If you control for the other variables, yes, a causal relationship can be established. That would mean doing a well-designed experiment. Otherwise, no. 11. Please interpret the correlation for this problem. (Remember the three things, and use the context of the problem) Very strong positive linear relationship 12. By looking at this scatter plot we can see that higher ages correspond with a higher vocabulary size. But just because two variables are correlated does not mean one CAUSES the other. Explain why this case is a good example of that. Age Vocabulary size 6 5 4 3 2 1 2500 2000 1500 1000 500 0 Scatterplot of Vocabulary size vs Age 2